I'm asking about someone who's employed by a company and does different jobs (both a qualified and unqualified person). Who knows; maybe in English those two are two different words? What are they called in English?

All I know is a navvy but that usually means physical work.

Let me just try a few things here. These are just wild guesses, nothing more.

In the broadest sense the person may be called a jack of all trades but I highly doubt this would be the title of a person at a company or the term the employees used. I have never heard anyone say "Oh let's assign that to our jack of all trades".
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RyeɃreḁdApr 12 '14 at 19:46

A Renaissance person is someone who works at many careers during his/her lifetime, possibly at the same time. The "Renaissance" part is because a lot of people (usually men) were like this during that period, such as Leonardo da Vinci, who was an artist, scientist, inventor, engineer, architect, and a whole bunch of other things. I suppose that, as it was a time of change, there were more unfilled "niches" for people to fill, and some people just happened to fill many at once, not to mention how low the barriers to entry for those jobs probably were, for a couple reasons.

We may be entering another "Renaissance", with regards to the Internet. For example, I'm answering this question on English.StackExchange, and I've answered several questions on StackOverflow, SuperUser, Security.StackExchange, and even Physics.StackExchange (although I haven't gotten money for any of them).

You can call such a person a one-man band. This expression emphasizes that the different jobs are performed simultaneously or nearly simultaneously while avoiding the possibly negative connotations of jack of all trades (jack of all trades, master of none).